Why are three of the five base location choices unavailable

Cars indeed have a damage threshold, 2 of them, even!

First threshold prevents it from catching fire or exploding. (Pistol hitting a car for example) Then once that one is passed the car catches fire. The second one is where it explodes straight away.

Things to remember when using cars for cover or shooting at them:

• Cars caught fire during your turn explode on your next turn.
• Cars caught fire during an enemy turn explode on their next turn.
• Cover remains after a car blew up!
• You can use grenades and rockets to target and blow up cars before using their cover.
• Kills done by cars are like grenades and rockets they yield no materials only a corpse (fragments)

From what I read, others report that grenades kill cars instantly, where in my games they never do that. It seems higher difficulty is higher threshold. I play impossible so as such I will not note my damage expectations and experiences.

It is in fact an event where you will get a chance to get more resources. This is really important; you need to acquire certain materials to do certain research to get a path to victory in the game, and that says nothing of getting your soldiers properly outfitted.

As to the randomness, that's not likely. The aliens have an agenda and it will play out on the geoscape. UFOs have missions; shooting them down prevents them from carrying those missions out. Allowing the aliens to carry out those missions will help spread panic/alien presence (at a high level) which is bad for you.

I have only ever seen ufos where I had satellites deployed. Eventually you will need to upgrade interceptors as they will start encountering much larger, more powerful craft.